In the test reports for biochar, the relationship between Total Carbon, Fixed Carbon, and Organic Carbon is similar to that in coal, but with nuances specific to biochar's characteristics (such as high carbon content and the potential presence of carbonates).

In short, the relationship can be summarized as:
Total Carbon ≈ Organic Carbon + Inorganic Carbon (a small amount)
Fixed Carbon ≈ Total Carbon - Carbon in Volatile Matter (and residues in ash)

Here is a detailed analysis specific to biochar:

1. Differences in Core Definitions in the Context of Biochar

Total Carbon:

This value is directly measured using an elemental analyzer. It represents the sum of all forms of carbon elements in the biochar sample.

In biochar, this includes carbon in the aromatic ring structure (the precursor to fixed carbon), carbon in adsorbed organic molecules, and carbon from carbonates (e.g., lime, soil mineral contamination) that may have been introduced by the feedstock or during production.

Organic Carbon:

This is the most important indicator in biochar research and agricultural applications. It represents the carbon's stability in soil, its carbon sequestration potential, and its contribution to soil fertility.

In testing, Organic Carbon is typically calculated by subtracting Inorganic Carbon (mainly carbonate carbon) from Total Carbon: Corganic=Ctotal−CinorganicCorganic=Ctotal−Cinorganic.

For high-quality, pristine biochar (e.g., from woody biomass produced at high temperatures), the inorganic carbon content is usually negligible. In this case, Total Carbon ≈ Organic Carbon.

Fixed Carbon:

This is an index calculated from Proximate Analysis.

Formula: FC=100%−(Moisture%+Ash%+VolatileMatter%)FC=100%−(Moisture%+Ash%+VolatileMatter%)

It represents the solid, highly stable, and difficult-to-decompose carbon skeleton that remains after the biochar is subjected to high temperatures in an inert atmosphere.

Key Difference: Fixed Carbon is a process indicator describing "how much solid residue remains when heated to a high temperature," while Organic Carbon is a chemical indicator describing "the total amount of carbon elements present." The volatile matter in biochar itself contains carbon, so Organic Carbon is always greater than Fixed Carbon.

2. Quantitative Relationship Among the Three in Biochar

For a typical high-temperature biochar made from woody feedstock at 500-600°C, the relationship is approximately:

Total Carbon(80%)≈Organic Carbon(79.5%)+Inorganic Carbon(0.5%)Total Carbon(80%)≈Organic Carbon(79.5%)+Inorganic Carbon(0.5%)Fixed Carbon(75%)≈Organic Carbon(79.5%)−Carbon in Volatile Matter(4.5%)Fixed Carbon(75%)≈Organic Carbon(79.5%)−Carbon in Volatile Matter(4.5%)

Typical Numerical Order:
Total Carbon ≥ Organic Carbon > Fixed Carbon

3. Why Do These Differences Exist? (From a Biochar Perspective)

Interference from Volatile Matter:

If the pyrolysis process during biochar production is incomplete, some tars or volatile organic molecules may remain.

This volatile matter contains carbon elements and is part of the Organic Carbon.

However, when measuring Fixed Carbon, this volatile matter is driven off by heating. Therefore, Fixed Carbon does not include it.

Conclusion: The Fixed Carbon value of biochar is always lower than its Organic Carbon value.

Effect of Ash:

The ash (mineral matter) in biochar contains no carbon. In the Fixed Carbon calculation, ash is already subtracted (as per the formula).

In the calculation of Organic Carbon (if using the difference method Ctotal−CinorganicCtotal−Cinorganic), ash does not affect the Organic Carbon value, as Organic Carbon only concerns "carbon elements."

Presence of Inorganic Carbon (Carbonates):

If the biochar feedstock is high in calcium (e.g., certain nut shells, some straws), or if the production temperature is extremely high (>700°C), calcium carbonate crystals may form.

The carbon in this carbonate is Inorganic Carbon. It is included in Total Carbon but is not part of Organic Carbon.

Simultaneously, this carbonate remains in the ash during the Proximate Analysis ash test, so it is also not part of Fixed Carbon.

4. Summary

Total Carbon tells you "how much carbon element is present in total."

Organic Carbon tells you "how much of this carbon comes from biomass and is beneficial for soil" (and is also the basis for stability).

Fixed Carbon tells you "how much of this carbon is extremely recalcitrant, forming a solid skeleton that doesn't burn away even at high temperatures" (representing stability).

When interpreting a biochar test report containing all three values:

If Total Carbon ≈ Organic Carbon, the biochar is pristine and contains no carbonates.

If Organic Carbon > Fixed Carbon, this is normal and indicates that some carbon is present in the volatile matter.

If Total Carbon is significantly greater than Organic Carbon (e.g., a difference >5%), it suggests the biochar might be mixed with lime or soil, leading to high inorganic carbon.

If Fixed Carbon is very close to Total Carbon, it indicates the biochar was produced at an extremely high temperature, resulting in very low volatile matter and minimal ash content.